TSTP Solution File: KLE101+1 by Vampire---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : KLE101+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% Computer : n005.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 05:36:48 EDT 2023
% Result : Theorem 4.32s 1.04s
% Output : Refutation 4.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 72
% Number of leaves : 39
% Syntax : Number of formulae : 212 ( 206 unt; 0 def)
% Number of atoms : 220 ( 219 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 18 ( 10 ~; 0 |; 4 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 29 ( 29 usr; 21 con; 0-2 aty)
% Number of variables : 152 (; 146 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f41778,plain,
$false,
inference(trivial_inequality_removal,[],[f40982]) ).
fof(f40982,plain,
zero != zero,
inference(backward_demodulation,[],[f93,f40980]) ).
fof(f40980,plain,
zero = sF12,
inference(forward_demodulation,[],[f40979,f54]) ).
fof(f54,plain,
! [X0] : multiplication(one,X0) = X0,
inference(cnf_transformation,[],[f7]) ).
fof(f7,axiom,
! [X0] : multiplication(one,X0) = X0,
file('/export/starexec/sandbox2/tmp/tmp.JoAmLo7DR6/Vampire---4.8_7230',multiplicative_left_identity) ).
fof(f40979,plain,
zero = multiplication(one,sF12),
inference(forward_demodulation,[],[f40978,f2727]) ).
fof(f2727,plain,
one = antidomain(multiplication(sF4,sF13)),
inference(backward_demodulation,[],[f1474,f2690]) ).
fof(f2690,plain,
! [X19] : one = addition(one,antidomain(X19)),
inference(forward_demodulation,[],[f2627,f63]) ).
fof(f63,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f1,axiom,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
file('/export/starexec/sandbox2/tmp/tmp.JoAmLo7DR6/Vampire---4.8_7230',additive_commutativity) ).
fof(f2627,plain,
! [X19] : one = addition(antidomain(X19),one),
inference(superposition,[],[f176,f157]) ).
fof(f157,plain,
! [X1] : one = addition(antidomain(X1),antidomain(antidomain(X1))),
inference(superposition,[],[f62,f63]) ).
fof(f62,plain,
! [X0] : one = addition(antidomain(antidomain(X0)),antidomain(X0)),
inference(cnf_transformation,[],[f36]) ).
fof(f36,plain,
! [X0] : one = addition(antidomain(antidomain(X0)),antidomain(X0)),
inference(rectify,[],[f15]) ).
fof(f15,axiom,
! [X3] : one = addition(antidomain(antidomain(X3)),antidomain(X3)),
file('/export/starexec/sandbox2/tmp/tmp.JoAmLo7DR6/Vampire---4.8_7230',domain3) ).
fof(f176,plain,
! [X2,X3] : addition(X2,X3) = addition(X2,addition(X2,X3)),
inference(superposition,[],[f71,f55]) ).
fof(f55,plain,
! [X0] : addition(X0,X0) = X0,
inference(cnf_transformation,[],[f4]) ).
fof(f4,axiom,
! [X0] : addition(X0,X0) = X0,
file('/export/starexec/sandbox2/tmp/tmp.JoAmLo7DR6/Vampire---4.8_7230',additive_idempotence) ).
fof(f71,plain,
! [X2,X0,X1] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
inference(cnf_transformation,[],[f44]) ).
fof(f44,plain,
! [X0,X1,X2] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
inference(rectify,[],[f2]) ).
fof(f2,axiom,
! [X2,X1,X0] : addition(X0,addition(X1,X2)) = addition(addition(X0,X1),X2),
file('/export/starexec/sandbox2/tmp/tmp.JoAmLo7DR6/Vampire---4.8_7230',additive_associativity) ).
fof(f1474,plain,
antidomain(multiplication(sF4,sF13)) = addition(one,antidomain(multiplication(sF4,sF13))),
inference(forward_demodulation,[],[f1473,f161]) ).
fof(f161,plain,
one = antidomain(zero),
inference(forward_demodulation,[],[f148,f52]) ).
fof(f52,plain,
! [X0] : addition(X0,zero) = X0,
inference(cnf_transformation,[],[f3]) ).
fof(f3,axiom,
! [X0] : addition(X0,zero) = X0,
file('/export/starexec/sandbox2/tmp/tmp.JoAmLo7DR6/Vampire---4.8_7230',additive_identity) ).
fof(f148,plain,
one = addition(antidomain(zero),zero),
inference(superposition,[],[f62,f116]) ).
fof(f116,plain,
zero = antidomain(one),
inference(superposition,[],[f57,f53]) ).
fof(f53,plain,
! [X0] : multiplication(X0,one) = X0,
inference(cnf_transformation,[],[f6]) ).
fof(f6,axiom,
! [X0] : multiplication(X0,one) = X0,
file('/export/starexec/sandbox2/tmp/tmp.JoAmLo7DR6/Vampire---4.8_7230',multiplicative_right_identity) ).
fof(f57,plain,
! [X0] : zero = multiplication(antidomain(X0),X0),
inference(cnf_transformation,[],[f31]) ).
fof(f31,plain,
! [X0] : zero = multiplication(antidomain(X0),X0),
inference(rectify,[],[f13]) ).
fof(f13,axiom,
! [X3] : zero = multiplication(antidomain(X3),X3),
file('/export/starexec/sandbox2/tmp/tmp.JoAmLo7DR6/Vampire---4.8_7230',domain1) ).
fof(f1473,plain,
antidomain(multiplication(sF4,sF13)) = addition(antidomain(zero),antidomain(multiplication(sF4,sF13))),
inference(forward_demodulation,[],[f1472,f94]) ).
fof(f94,plain,
antidomain(sF4) = sF13,
introduced(function_definition,[]) ).
fof(f1472,plain,
antidomain(multiplication(sF4,antidomain(sF4))) = addition(antidomain(zero),antidomain(multiplication(sF4,antidomain(sF4)))),
inference(forward_demodulation,[],[f1383,f84]) ).
fof(f84,plain,
antidomain(sF3) = sF4,
introduced(function_definition,[]) ).
fof(f1383,plain,
antidomain(multiplication(sF4,antidomain(antidomain(sF3)))) = addition(antidomain(zero),antidomain(multiplication(sF4,antidomain(antidomain(sF3))))),
inference(superposition,[],[f70,f110]) ).
fof(f110,plain,
zero = multiplication(sF4,sF3),
inference(superposition,[],[f57,f84]) ).
fof(f70,plain,
! [X0,X1] : antidomain(multiplication(X0,antidomain(antidomain(X1)))) = addition(antidomain(multiplication(X0,X1)),antidomain(multiplication(X0,antidomain(antidomain(X1))))),
inference(cnf_transformation,[],[f43]) ).
fof(f43,plain,
! [X0,X1] : antidomain(multiplication(X0,antidomain(antidomain(X1)))) = addition(antidomain(multiplication(X0,X1)),antidomain(multiplication(X0,antidomain(antidomain(X1))))),
inference(rectify,[],[f14]) ).
fof(f14,axiom,
! [X3,X4] : antidomain(multiplication(X3,antidomain(antidomain(X4)))) = addition(antidomain(multiplication(X3,X4)),antidomain(multiplication(X3,antidomain(antidomain(X4))))),
file('/export/starexec/sandbox2/tmp/tmp.JoAmLo7DR6/Vampire---4.8_7230',domain2) ).
fof(f40978,plain,
zero = multiplication(antidomain(multiplication(sF4,sF13)),sF12),
inference(forward_demodulation,[],[f40973,f57]) ).
fof(f40973,plain,
multiplication(antidomain(multiplication(sF4,sF13)),sF12) = multiplication(antidomain(multiplication(sF4,sF13)),multiplication(sF4,sF13)),
inference(superposition,[],[f488,f33193]) ).
fof(f33193,plain,
multiplication(sF4,sF13) = addition(sF12,multiplication(sF4,sF13)),
inference(superposition,[],[f381,f33076]) ).
fof(f33076,plain,
sF13 = addition(sF11,sF13),
inference(forward_demodulation,[],[f33014,f53]) ).
fof(f33014,plain,
multiplication(sF13,one) = addition(sF11,sF13),
inference(superposition,[],[f31216,f53]) ).
fof(f31216,plain,
! [X19] : multiplication(sF13,X19) = multiplication(addition(sF11,sF13),X19),
inference(forward_demodulation,[],[f31215,f54]) ).
fof(f31215,plain,
! [X19] : multiplication(addition(sF11,sF13),X19) = multiplication(one,multiplication(sF13,X19)),
inference(forward_demodulation,[],[f31214,f2795]) ).
fof(f2795,plain,
one = addition(one,sF11),
inference(forward_demodulation,[],[f2655,f63]) ).
fof(f2655,plain,
one = addition(sF11,one),
inference(superposition,[],[f176,f143]) ).
fof(f143,plain,
one = addition(sF11,coantidomain(sF11)),
inference(forward_demodulation,[],[f132,f63]) ).
fof(f132,plain,
one = addition(coantidomain(sF11),sF11),
inference(superposition,[],[f61,f91]) ).
fof(f91,plain,
coantidomain(sF10) = sF11,
introduced(function_definition,[]) ).
fof(f61,plain,
! [X0] : one = addition(coantidomain(coantidomain(X0)),coantidomain(X0)),
inference(cnf_transformation,[],[f35]) ).
fof(f35,plain,
! [X0] : one = addition(coantidomain(coantidomain(X0)),coantidomain(X0)),
inference(rectify,[],[f19]) ).
fof(f19,axiom,
! [X3] : one = addition(coantidomain(coantidomain(X3)),coantidomain(X3)),
file('/export/starexec/sandbox2/tmp/tmp.JoAmLo7DR6/Vampire---4.8_7230',codomain3) ).
fof(f31214,plain,
! [X19] : multiplication(addition(one,sF11),multiplication(sF13,X19)) = multiplication(addition(sF11,sF13),X19),
inference(forward_demodulation,[],[f31213,f74]) ).
fof(f74,plain,
! [X2,X0,X1] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
inference(cnf_transformation,[],[f9]) ).
fof(f9,axiom,
! [X0,X1,X2] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
file('/export/starexec/sandbox2/tmp/tmp.JoAmLo7DR6/Vampire---4.8_7230',left_distributivity) ).
fof(f31213,plain,
! [X19] : multiplication(addition(one,sF11),multiplication(sF13,X19)) = addition(multiplication(sF11,X19),multiplication(sF13,X19)),
inference(forward_demodulation,[],[f31163,f63]) ).
fof(f31163,plain,
! [X19] : multiplication(addition(one,sF11),multiplication(sF13,X19)) = addition(multiplication(sF13,X19),multiplication(sF11,X19)),
inference(superposition,[],[f638,f26048]) ).
fof(f26048,plain,
! [X0] : multiplication(sF11,X0) = multiplication(sF11,multiplication(sF13,X0)),
inference(superposition,[],[f72,f26021]) ).
fof(f26021,plain,
sF11 = multiplication(sF11,sF13),
inference(forward_demodulation,[],[f25998,f53]) ).
fof(f25998,plain,
multiplication(sF11,one) = multiplication(sF11,sF13),
inference(superposition,[],[f17598,f169]) ).
fof(f169,plain,
one = addition(sF13,sF14),
inference(forward_demodulation,[],[f168,f95]) ).
fof(f95,plain,
antidomain(sF13) = sF14,
introduced(function_definition,[]) ).
fof(f168,plain,
one = addition(sF13,antidomain(sF13)),
inference(forward_demodulation,[],[f152,f63]) ).
fof(f152,plain,
one = addition(antidomain(sF13),sF13),
inference(superposition,[],[f62,f94]) ).
fof(f17598,plain,
! [X2] : multiplication(sF11,X2) = multiplication(sF11,addition(X2,sF14)),
inference(forward_demodulation,[],[f17586,f52]) ).
fof(f17586,plain,
! [X2] : multiplication(sF11,addition(X2,sF14)) = addition(multiplication(sF11,X2),zero),
inference(superposition,[],[f73,f17559]) ).
fof(f17559,plain,
zero = multiplication(sF11,sF14),
inference(forward_demodulation,[],[f17549,f53]) ).
fof(f17549,plain,
zero = multiplication(sF11,multiplication(sF14,one)),
inference(superposition,[],[f267,f17521]) ).
fof(f17521,plain,
one = coantidomain(multiplication(sF11,sF14)),
inference(forward_demodulation,[],[f17520,f2743]) ).
fof(f2743,plain,
! [X23] : one = addition(one,coantidomain(X23)),
inference(forward_demodulation,[],[f2630,f63]) ).
fof(f2630,plain,
! [X23] : one = addition(coantidomain(X23),one),
inference(superposition,[],[f176,f133]) ).
fof(f133,plain,
! [X1] : one = addition(coantidomain(X1),coantidomain(coantidomain(X1))),
inference(superposition,[],[f61,f63]) ).
fof(f17520,plain,
coantidomain(multiplication(sF11,sF14)) = addition(one,coantidomain(multiplication(sF11,sF14))),
inference(forward_demodulation,[],[f17519,f137]) ).
fof(f137,plain,
one = coantidomain(zero),
inference(forward_demodulation,[],[f128,f52]) ).
fof(f128,plain,
one = addition(coantidomain(zero),zero),
inference(superposition,[],[f61,f106]) ).
fof(f106,plain,
zero = coantidomain(one),
inference(superposition,[],[f56,f54]) ).
fof(f56,plain,
! [X0] : zero = multiplication(X0,coantidomain(X0)),
inference(cnf_transformation,[],[f30]) ).
fof(f30,plain,
! [X0] : zero = multiplication(X0,coantidomain(X0)),
inference(rectify,[],[f17]) ).
fof(f17,axiom,
! [X3] : zero = multiplication(X3,coantidomain(X3)),
file('/export/starexec/sandbox2/tmp/tmp.JoAmLo7DR6/Vampire---4.8_7230',codomain1) ).
fof(f17519,plain,
coantidomain(multiplication(sF11,sF14)) = addition(coantidomain(zero),coantidomain(multiplication(sF11,sF14))),
inference(forward_demodulation,[],[f17518,f91]) ).
fof(f17518,plain,
coantidomain(multiplication(coantidomain(sF10),sF14)) = addition(coantidomain(zero),coantidomain(multiplication(coantidomain(sF10),sF14))),
inference(forward_demodulation,[],[f17509,f90]) ).
fof(f90,plain,
coantidomain(sF9) = sF10,
introduced(function_definition,[]) ).
fof(f17509,plain,
coantidomain(multiplication(coantidomain(coantidomain(sF9)),sF14)) = addition(coantidomain(zero),coantidomain(multiplication(coantidomain(coantidomain(sF9)),sF14))),
inference(superposition,[],[f69,f17487]) ).
fof(f17487,plain,
zero = multiplication(sF9,sF14),
inference(backward_demodulation,[],[f3406,f17484]) ).
fof(f17484,plain,
zero = multiplication(sF8,sF15),
inference(forward_demodulation,[],[f17474,f53]) ).
fof(f17474,plain,
zero = multiplication(sF8,multiplication(sF15,one)),
inference(superposition,[],[f267,f17013]) ).
fof(f17013,plain,
one = coantidomain(multiplication(sF8,sF15)),
inference(forward_demodulation,[],[f17012,f2743]) ).
fof(f17012,plain,
coantidomain(multiplication(sF8,sF15)) = addition(one,coantidomain(multiplication(sF8,sF15))),
inference(forward_demodulation,[],[f17011,f137]) ).
fof(f17011,plain,
coantidomain(multiplication(sF8,sF15)) = addition(coantidomain(zero),coantidomain(multiplication(sF8,sF15))),
inference(forward_demodulation,[],[f17010,f88]) ).
fof(f88,plain,
coantidomain(sF7) = sF8,
introduced(function_definition,[]) ).
fof(f17010,plain,
coantidomain(multiplication(coantidomain(sF7),sF15)) = addition(coantidomain(zero),coantidomain(multiplication(coantidomain(sF7),sF15))),
inference(forward_demodulation,[],[f16996,f87]) ).
fof(f87,plain,
coantidomain(sF6) = sF7,
introduced(function_definition,[]) ).
fof(f16996,plain,
coantidomain(multiplication(coantidomain(coantidomain(sF6)),sF15)) = addition(coantidomain(zero),coantidomain(multiplication(coantidomain(coantidomain(sF6)),sF15))),
inference(superposition,[],[f69,f16955]) ).
fof(f16955,plain,
zero = multiplication(sF6,sF15),
inference(forward_demodulation,[],[f16914,f50]) ).
fof(f50,plain,
! [X0] : zero = multiplication(X0,zero),
inference(cnf_transformation,[],[f10]) ).
fof(f10,axiom,
! [X0] : zero = multiplication(X0,zero),
file('/export/starexec/sandbox2/tmp/tmp.JoAmLo7DR6/Vampire---4.8_7230',right_annihilation) ).
fof(f16914,plain,
multiplication(sF6,zero) = multiplication(sF6,sF15),
inference(superposition,[],[f12082,f114]) ).
fof(f114,plain,
zero = multiplication(sF16,sF15),
inference(superposition,[],[f57,f97]) ).
fof(f97,plain,
antidomain(sF15) = sF16,
introduced(function_definition,[]) ).
fof(f12082,plain,
! [X3] : multiplication(sF6,X3) = multiplication(sF6,multiplication(sF16,X3)),
inference(superposition,[],[f72,f12049]) ).
fof(f12049,plain,
sF6 = multiplication(sF6,sF16),
inference(forward_demodulation,[],[f12019,f53]) ).
fof(f12019,plain,
multiplication(sF6,one) = multiplication(sF6,sF16),
inference(superposition,[],[f7430,f173]) ).
fof(f173,plain,
one = addition(sF16,sF17),
inference(forward_demodulation,[],[f172,f98]) ).
fof(f98,plain,
antidomain(sF16) = sF17,
introduced(function_definition,[]) ).
fof(f172,plain,
one = addition(sF16,antidomain(sF16)),
inference(forward_demodulation,[],[f155,f63]) ).
fof(f155,plain,
one = addition(antidomain(sF16),sF16),
inference(superposition,[],[f62,f97]) ).
fof(f7430,plain,
! [X5] : multiplication(sF6,X5) = multiplication(sF6,addition(X5,sF17)),
inference(forward_demodulation,[],[f7412,f52]) ).
fof(f7412,plain,
! [X5] : multiplication(sF6,addition(X5,sF17)) = addition(multiplication(sF6,X5),zero),
inference(superposition,[],[f73,f7380]) ).
fof(f7380,plain,
zero = multiplication(sF6,sF17),
inference(superposition,[],[f281,f7272]) ).
fof(f7272,plain,
sF17 = multiplication(sF5,sF17),
inference(forward_demodulation,[],[f7181,f54]) ).
fof(f7181,plain,
multiplication(sF5,sF17) = multiplication(one,sF17),
inference(superposition,[],[f773,f2595]) ).
fof(f2595,plain,
one = addition(sF5,antidomain(sF17)),
inference(backward_demodulation,[],[f2266,f2593]) ).
fof(f2593,plain,
one = addition(one,sF5),
inference(forward_demodulation,[],[f2592,f63]) ).
fof(f2592,plain,
one = addition(sF5,one),
inference(forward_demodulation,[],[f2584,f2163]) ).
fof(f2163,plain,
one = addition(sF5,sF16),
inference(forward_demodulation,[],[f2162,f173]) ).
fof(f2162,plain,
addition(sF16,sF17) = addition(sF5,sF16),
inference(forward_demodulation,[],[f2149,f63]) ).
fof(f2149,plain,
addition(sF17,sF16) = addition(sF5,sF16),
inference(superposition,[],[f2072,f2126]) ).
fof(f2126,plain,
sF16 = addition(sF16,multiplication(sF16,sF5)),
inference(forward_demodulation,[],[f2119,f1790]) ).
fof(f1790,plain,
sF16 = addition(sF6,multiplication(sF16,sF5)),
inference(forward_demodulation,[],[f1779,f53]) ).
fof(f1779,plain,
multiplication(sF16,one) = addition(sF6,multiplication(sF16,sF5)),
inference(superposition,[],[f872,f165]) ).
fof(f165,plain,
one = addition(sF5,sF6),
inference(forward_demodulation,[],[f164,f86]) ).
fof(f86,plain,
antidomain(sF5) = sF6,
introduced(function_definition,[]) ).
fof(f164,plain,
one = addition(sF5,antidomain(sF5)),
inference(forward_demodulation,[],[f150,f63]) ).
fof(f150,plain,
one = addition(antidomain(sF5),sF5),
inference(superposition,[],[f62,f85]) ).
fof(f85,plain,
antidomain(sK2) = sF5,
introduced(function_definition,[]) ).
fof(f872,plain,
! [X2] : multiplication(sF16,addition(X2,sF6)) = addition(sF6,multiplication(sF16,X2)),
inference(forward_demodulation,[],[f868,f63]) ).
fof(f868,plain,
! [X2] : multiplication(sF16,addition(X2,sF6)) = addition(multiplication(sF16,X2),sF6),
inference(superposition,[],[f73,f859]) ).
fof(f859,plain,
sF6 = multiplication(sF16,sF6),
inference(forward_demodulation,[],[f852,f54]) ).
fof(f852,plain,
multiplication(one,sF6) = multiplication(sF16,sF6),
inference(superposition,[],[f816,f173]) ).
fof(f816,plain,
! [X69] : multiplication(X69,sF6) = multiplication(addition(X69,sF17),sF6),
inference(forward_demodulation,[],[f721,f52]) ).
fof(f721,plain,
! [X69] : multiplication(addition(X69,sF17),sF6) = addition(multiplication(X69,sF6),zero),
inference(superposition,[],[f74,f101]) ).
fof(f101,plain,
zero = multiplication(sF17,sF6),
inference(backward_demodulation,[],[f99,f100]) ).
fof(f100,plain,
zero = sF18,
inference(definition_folding,[],[f82,f99,f86,f85,f98,f97,f96,f95,f94,f84,f83]) ).
fof(f83,plain,
antidomain(sK1) = sF3,
introduced(function_definition,[]) ).
fof(f96,plain,
multiplication(sK0,sF14) = sF15,
introduced(function_definition,[]) ).
fof(f82,plain,
zero = multiplication(antidomain(antidomain(multiplication(sK0,antidomain(antidomain(antidomain(antidomain(sK1))))))),antidomain(antidomain(sK2))),
inference(definition_unfolding,[],[f48,f79,f60,f60]) ).
fof(f60,plain,
! [X0] : domain(X0) = antidomain(antidomain(X0)),
inference(cnf_transformation,[],[f34]) ).
fof(f34,plain,
! [X0] : domain(X0) = antidomain(antidomain(X0)),
inference(rectify,[],[f16]) ).
fof(f16,axiom,
! [X3] : antidomain(antidomain(X3)) = domain(X3),
file('/export/starexec/sandbox2/tmp/tmp.JoAmLo7DR6/Vampire---4.8_7230',domain4) ).
fof(f79,plain,
! [X0,X1] : forward_diamond(X0,X1) = antidomain(antidomain(multiplication(X0,antidomain(antidomain(X1))))),
inference(definition_unfolding,[],[f68,f60,f60]) ).
fof(f68,plain,
! [X0,X1] : forward_diamond(X0,X1) = domain(multiplication(X0,domain(X1))),
inference(cnf_transformation,[],[f41]) ).
fof(f41,plain,
! [X0,X1] : forward_diamond(X0,X1) = domain(multiplication(X0,domain(X1))),
inference(rectify,[],[f23]) ).
fof(f23,axiom,
! [X3,X4] : forward_diamond(X3,X4) = domain(multiplication(X3,domain(X4))),
file('/export/starexec/sandbox2/tmp/tmp.JoAmLo7DR6/Vampire---4.8_7230',forward_diamond) ).
fof(f48,plain,
zero = multiplication(forward_diamond(sK0,domain(sK1)),domain(sK2)),
inference(cnf_transformation,[],[f47]) ).
fof(f47,plain,
( zero != multiplication(domain(sK1),backward_diamond(sK0,domain(sK2)))
& zero = multiplication(forward_diamond(sK0,domain(sK1)),domain(sK2)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f45,f46]) ).
fof(f46,plain,
( ? [X0,X1,X2] :
( zero != multiplication(domain(X1),backward_diamond(X0,domain(X2)))
& zero = multiplication(forward_diamond(X0,domain(X1)),domain(X2)) )
=> ( zero != multiplication(domain(sK1),backward_diamond(sK0,domain(sK2)))
& zero = multiplication(forward_diamond(sK0,domain(sK1)),domain(sK2)) ) ),
introduced(choice_axiom,[]) ).
fof(f45,plain,
? [X0,X1,X2] :
( zero != multiplication(domain(X1),backward_diamond(X0,domain(X2)))
& zero = multiplication(forward_diamond(X0,domain(X1)),domain(X2)) ),
inference(ennf_transformation,[],[f29]) ).
fof(f29,plain,
~ ! [X0,X1,X2] :
( zero = multiplication(forward_diamond(X0,domain(X1)),domain(X2))
=> zero = multiplication(domain(X1),backward_diamond(X0,domain(X2))) ),
inference(rectify,[],[f28]) ).
fof(f28,negated_conjecture,
~ ! [X3,X4,X5] :
( zero = multiplication(forward_diamond(X3,domain(X4)),domain(X5))
=> zero = multiplication(domain(X4),backward_diamond(X3,domain(X5))) ),
inference(negated_conjecture,[],[f27]) ).
fof(f27,conjecture,
! [X3,X4,X5] :
( zero = multiplication(forward_diamond(X3,domain(X4)),domain(X5))
=> zero = multiplication(domain(X4),backward_diamond(X3,domain(X5))) ),
file('/export/starexec/sandbox2/tmp/tmp.JoAmLo7DR6/Vampire---4.8_7230',goals) ).
fof(f99,plain,
multiplication(sF17,sF6) = sF18,
introduced(function_definition,[]) ).
fof(f2119,plain,
addition(sF6,multiplication(sF16,sF5)) = addition(sF16,multiplication(sF16,sF5)),
inference(superposition,[],[f1803,f55]) ).
fof(f1803,plain,
! [X0] : addition(sF16,X0) = addition(sF6,addition(multiplication(sF16,sF5),X0)),
inference(superposition,[],[f71,f1790]) ).
fof(f2072,plain,
! [X2] : addition(sF5,X2) = addition(sF17,addition(X2,multiplication(sF16,sF5))),
inference(superposition,[],[f1663,f63]) ).
fof(f1663,plain,
! [X0] : addition(sF5,X0) = addition(sF17,addition(multiplication(sF16,sF5),X0)),
inference(superposition,[],[f71,f1647]) ).
fof(f1647,plain,
sF5 = addition(sF17,multiplication(sF16,sF5)),
inference(forward_demodulation,[],[f1636,f54]) ).
fof(f1636,plain,
multiplication(one,sF5) = addition(sF17,multiplication(sF16,sF5)),
inference(superposition,[],[f815,f173]) ).
fof(f815,plain,
! [X68] : addition(sF17,multiplication(X68,sF5)) = multiplication(addition(X68,sF17),sF5),
inference(forward_demodulation,[],[f720,f63]) ).
fof(f720,plain,
! [X68] : multiplication(addition(X68,sF17),sF5) = addition(multiplication(X68,sF5),sF17),
inference(superposition,[],[f74,f546]) ).
fof(f546,plain,
sF17 = multiplication(sF17,sF5),
inference(forward_demodulation,[],[f541,f53]) ).
fof(f541,plain,
multiplication(sF17,one) = multiplication(sF17,sF5),
inference(superposition,[],[f513,f165]) ).
fof(f513,plain,
! [X49] : multiplication(sF17,X49) = multiplication(sF17,addition(X49,sF6)),
inference(forward_demodulation,[],[f436,f52]) ).
fof(f436,plain,
! [X49] : multiplication(sF17,addition(X49,sF6)) = addition(multiplication(sF17,X49),zero),
inference(superposition,[],[f73,f101]) ).
fof(f2584,plain,
addition(sF5,one) = addition(sF5,sF16),
inference(superposition,[],[f2262,f173]) ).
fof(f2262,plain,
! [X2] : addition(sF5,X2) = addition(sF5,addition(X2,sF17)),
inference(superposition,[],[f2170,f63]) ).
fof(f2170,plain,
! [X0] : addition(sF5,X0) = addition(sF5,addition(sF17,X0)),
inference(superposition,[],[f71,f2159]) ).
fof(f2159,plain,
sF5 = addition(sF5,sF17),
inference(forward_demodulation,[],[f2158,f55]) ).
fof(f2158,plain,
addition(sF5,sF5) = addition(sF5,sF17),
inference(forward_demodulation,[],[f2147,f63]) ).
fof(f2147,plain,
addition(sF5,sF5) = addition(sF17,sF5),
inference(superposition,[],[f2072,f2080]) ).
fof(f2080,plain,
sF5 = addition(sF5,multiplication(sF16,sF5)),
inference(forward_demodulation,[],[f2071,f1647]) ).
fof(f2071,plain,
addition(sF17,multiplication(sF16,sF5)) = addition(sF5,multiplication(sF16,sF5)),
inference(superposition,[],[f1663,f55]) ).
fof(f2266,plain,
addition(one,sF5) = addition(sF5,antidomain(sF17)),
inference(forward_demodulation,[],[f2254,f63]) ).
fof(f2254,plain,
addition(sF5,one) = addition(sF5,antidomain(sF17)),
inference(superposition,[],[f2170,f174]) ).
fof(f174,plain,
one = addition(sF17,antidomain(sF17)),
inference(forward_demodulation,[],[f156,f63]) ).
fof(f156,plain,
one = addition(antidomain(sF17),sF17),
inference(superposition,[],[f62,f98]) ).
fof(f773,plain,
! [X14,X15] : multiplication(X15,X14) = multiplication(addition(X15,antidomain(X14)),X14),
inference(forward_demodulation,[],[f684,f52]) ).
fof(f684,plain,
! [X14,X15] : multiplication(addition(X15,antidomain(X14)),X14) = addition(multiplication(X15,X14),zero),
inference(superposition,[],[f74,f57]) ).
fof(f281,plain,
! [X22] : zero = multiplication(sF6,multiplication(sF5,X22)),
inference(forward_demodulation,[],[f255,f51]) ).
fof(f51,plain,
! [X0] : zero = multiplication(zero,X0),
inference(cnf_transformation,[],[f11]) ).
fof(f11,axiom,
! [X0] : zero = multiplication(zero,X0),
file('/export/starexec/sandbox2/tmp/tmp.JoAmLo7DR6/Vampire---4.8_7230',left_annihilation) ).
fof(f255,plain,
! [X22] : multiplication(sF6,multiplication(sF5,X22)) = multiplication(zero,X22),
inference(superposition,[],[f72,f112]) ).
fof(f112,plain,
zero = multiplication(sF6,sF5),
inference(superposition,[],[f57,f86]) ).
fof(f3406,plain,
multiplication(sF9,sF14) = multiplication(sF8,sF15),
inference(superposition,[],[f257,f96]) ).
fof(f257,plain,
! [X24] : multiplication(sF8,multiplication(sK0,X24)) = multiplication(sF9,X24),
inference(superposition,[],[f72,f89]) ).
fof(f89,plain,
multiplication(sF8,sK0) = sF9,
introduced(function_definition,[]) ).
fof(f69,plain,
! [X0,X1] : coantidomain(multiplication(coantidomain(coantidomain(X0)),X1)) = addition(coantidomain(multiplication(X0,X1)),coantidomain(multiplication(coantidomain(coantidomain(X0)),X1))),
inference(cnf_transformation,[],[f42]) ).
fof(f42,plain,
! [X0,X1] : coantidomain(multiplication(coantidomain(coantidomain(X0)),X1)) = addition(coantidomain(multiplication(X0,X1)),coantidomain(multiplication(coantidomain(coantidomain(X0)),X1))),
inference(rectify,[],[f18]) ).
fof(f18,axiom,
! [X3,X4] : coantidomain(multiplication(coantidomain(coantidomain(X3)),X4)) = addition(coantidomain(multiplication(X3,X4)),coantidomain(multiplication(coantidomain(coantidomain(X3)),X4))),
file('/export/starexec/sandbox2/tmp/tmp.JoAmLo7DR6/Vampire---4.8_7230',codomain2) ).
fof(f267,plain,
! [X8,X7] : zero = multiplication(X7,multiplication(X8,coantidomain(multiplication(X7,X8)))),
inference(superposition,[],[f72,f56]) ).
fof(f73,plain,
! [X2,X0,X1] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
inference(cnf_transformation,[],[f8]) ).
fof(f8,axiom,
! [X0,X1,X2] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
file('/export/starexec/sandbox2/tmp/tmp.JoAmLo7DR6/Vampire---4.8_7230',right_distributivity) ).
fof(f72,plain,
! [X2,X0,X1] : multiplication(X0,multiplication(X1,X2)) = multiplication(multiplication(X0,X1),X2),
inference(cnf_transformation,[],[f5]) ).
fof(f5,axiom,
! [X0,X1,X2] : multiplication(X0,multiplication(X1,X2)) = multiplication(multiplication(X0,X1),X2),
file('/export/starexec/sandbox2/tmp/tmp.JoAmLo7DR6/Vampire---4.8_7230',multiplicative_associativity) ).
fof(f638,plain,
! [X12,X13] : multiplication(addition(one,X13),X12) = addition(X12,multiplication(X13,X12)),
inference(superposition,[],[f74,f54]) ).
fof(f381,plain,
! [X20] : multiplication(sF4,addition(sF11,X20)) = addition(sF12,multiplication(sF4,X20)),
inference(superposition,[],[f73,f92]) ).
fof(f92,plain,
multiplication(sF4,sF11) = sF12,
introduced(function_definition,[]) ).
fof(f488,plain,
! [X14,X15] : multiplication(antidomain(X14),X15) = multiplication(antidomain(X14),addition(X15,X14)),
inference(forward_demodulation,[],[f411,f52]) ).
fof(f411,plain,
! [X14,X15] : multiplication(antidomain(X14),addition(X15,X14)) = addition(multiplication(antidomain(X14),X15),zero),
inference(superposition,[],[f73,f57]) ).
fof(f93,plain,
zero != sF12,
inference(definition_folding,[],[f81,f92,f91,f90,f89,f88,f87,f86,f85,f84,f83]) ).
fof(f81,plain,
zero != multiplication(antidomain(antidomain(sK1)),coantidomain(coantidomain(multiplication(coantidomain(coantidomain(antidomain(antidomain(sK2)))),sK0)))),
inference(definition_unfolding,[],[f49,f60,f76,f60]) ).
fof(f76,plain,
! [X0,X1] : backward_diamond(X0,X1) = coantidomain(coantidomain(multiplication(coantidomain(coantidomain(X1)),X0))),
inference(definition_unfolding,[],[f67,f59,f59]) ).
fof(f59,plain,
! [X0] : coantidomain(coantidomain(X0)) = codomain(X0),
inference(cnf_transformation,[],[f33]) ).
fof(f33,plain,
! [X0] : coantidomain(coantidomain(X0)) = codomain(X0),
inference(rectify,[],[f20]) ).
fof(f20,axiom,
! [X3] : coantidomain(coantidomain(X3)) = codomain(X3),
file('/export/starexec/sandbox2/tmp/tmp.JoAmLo7DR6/Vampire---4.8_7230',codomain4) ).
fof(f67,plain,
! [X0,X1] : backward_diamond(X0,X1) = codomain(multiplication(codomain(X1),X0)),
inference(cnf_transformation,[],[f40]) ).
fof(f40,plain,
! [X0,X1] : backward_diamond(X0,X1) = codomain(multiplication(codomain(X1),X0)),
inference(rectify,[],[f24]) ).
fof(f24,axiom,
! [X3,X4] : backward_diamond(X3,X4) = codomain(multiplication(codomain(X4),X3)),
file('/export/starexec/sandbox2/tmp/tmp.JoAmLo7DR6/Vampire---4.8_7230',backward_diamond) ).
fof(f49,plain,
zero != multiplication(domain(sK1),backward_diamond(sK0,domain(sK2))),
inference(cnf_transformation,[],[f47]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : KLE101+1 : TPTP v8.1.2. Released v4.0.0.
% 0.12/0.15 % Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.15/0.36 % Computer : n005.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Tue Aug 29 11:37:53 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.15/0.36 This is a FOF_THM_RFO_SEQ problem
% 0.15/0.37 Running vampire_casc2023 --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/tmp/tmp.JoAmLo7DR6/Vampire---4.8_7230
% 0.15/0.37 % (7369)Running in auto input_syntax mode. Trying TPTP
% 0.23/0.43 % (7386)ott+11_14_av=off:bs=on:bsr=on:cond=on:flr=on:fsd=off:fde=unused:gsp=on:nm=4:nwc=1.5:tgt=full_501 on Vampire---4 for (501ds/0Mi)
% 0.23/0.43 % (7372)lrs+10_11_cond=on:drc=off:flr=on:fsr=off:gsp=on:gs=on:gsem=off:lma=on:msp=off:nm=4:nwc=1.5:nicw=on:sas=z3:sims=off:sp=scramble:stl=188_1169 on Vampire---4 for (1169ds/0Mi)
% 0.23/0.43 % (7382)lrs+3_20_av=off:bd=preordered:drc=off:fsd=off:fsr=off:fde=unused:irw=on:lcm=reverse:sos=theory:stl=315_961 on Vampire---4 for (961ds/0Mi)
% 0.23/0.43 % (7379)ott-4_11_av=off:bd=preordered:bce=on:drc=off:flr=on:fsr=off:lma=on:nwc=2.0:sp=occurrence:tgt=ground:urr=ec_only_1010 on Vampire---4 for (1010ds/0Mi)
% 0.23/0.43 % (7385)lrs-11_32_av=off:bd=off:bs=on:bsr=on:drc=off:flr=on:fsd=off:fsr=off:fde=none:gsp=on:irw=on:lcm=predicate:nm=4:sp=scramble:stl=125_825 on Vampire---4 for (825ds/0Mi)
% 0.23/0.44 % (7384)ott+1003_4:1_av=off:cond=on:drc=off:fsd=off:fsr=off:fde=none:gsp=on:nm=2:nwc=1.5:sos=all:sp=reverse_arity:tgt=full_871 on Vampire---4 for (871ds/0Mi)
% 0.23/0.46 % (7376)lrs-11_28_aac=none:afr=on:anc=none:bs=on:drc=off:fde=unused:gs=on:nm=2:nwc=1.3:sp=frequency:stl=188_1092 on Vampire---4 for (1092ds/0Mi)
% 4.32/1.03 % (7379)First to succeed.
% 4.32/1.04 % (7379)Refutation found. Thanks to Tanya!
% 4.32/1.04 % SZS status Theorem for Vampire---4
% 4.32/1.04 % SZS output start Proof for Vampire---4
% See solution above
% 4.32/1.04 % (7379)------------------------------
% 4.32/1.04 % (7379)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 4.32/1.04 % (7379)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 4.32/1.04 % (7379)Termination reason: Refutation
% 4.32/1.04
% 4.32/1.04 % (7379)Memory used [KB]: 25841
% 4.32/1.04 % (7379)Time elapsed: 0.605 s
% 4.32/1.04 % (7379)------------------------------
% 4.32/1.04 % (7379)------------------------------
% 4.32/1.04 % (7369)Success in time 0.669 s
% 4.32/1.04 % Vampire---4.8 exiting
%------------------------------------------------------------------------------